Artificial compressibility based CBS solutions for double diffusive natural convection in cavities

Purpose – The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal temperature and concentration gradients, and validate the results against numerical and experimental data available from literature.Design/methodology/approach – The fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) scheme is adopted to solve double diffusion (DD) problems. A stabilization analysis is carried out to efficiently solve the problems considered in the present work. The thermal and solutal buoyancy forces acting on the fluid have been taken into account in case of aiding and opposing flow conditions.Findings – The stability limits derived by the authors for the thermo‐solutal convection assume a fundamental role to efficiently solve the DD problems considered. In the cases characterized by higher Rayleigh number the convergent solution is obtained only by employing the new st...

[1]  O. C. Zienkiewicz,et al.  The Finite Element Method for Fluid Dynamics , 2005 .

[2]  Y. Morsi,et al.  Natural convection inside dome shaped enclosures , 2002 .

[3]  M. Mansour,et al.  Effect of sinusoidal variations of boundary conditions on unsteady double diffusive convection in a square enclosure filled with a porous medium , 2012 .

[4]  K. N. Seetharamu,et al.  Fundamentals of the Finite Element Method for Heat and Fluid Flow , 2004 .

[5]  Ali J. Chamkha,et al.  Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients , 2002 .

[6]  Fausto Arpino,et al.  Transient Thermal Analysis of Natural Convection in Porous and Partially Porous Cavities , 2015 .

[7]  R. Bennacer,et al.  Double diffusion, natural convection in an enclosure filled with saturated porous medium subjected to cross gradients; stably stratified fluid , 2002 .

[8]  Hwataik Han,et al.  Double diffusive natural convection in a vertical rectangular enclosureII. Numerical study , 1991 .

[9]  Orhan Aydin,et al.  Natural convection in enclosures with localized heating from below and symmetrical cooling from sides , 2000 .

[10]  E. Papanicolaou,et al.  Double-diffusive natural convection in an asymmetric trapezoidal enclosure: unsteady behavior in the laminar and the turbulent-flow regime , 2005 .

[11]  P. Nithiarasu An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows , 2003 .

[12]  P. Prinos,et al.  Natural convection in an inclined enclosure , 1997 .

[13]  Di Liu,et al.  Natural convection in a porous enclosure with a partial heating and salting element , 2008 .

[14]  R. Viskanta,et al.  Natural Convection in Binary Gases Due to Horizontal Thermal and Solutal Gradients , 1991 .

[15]  D. Gobin,et al.  Cooperating thermosolutal convection in enclosures—II. Heat transfer and flow structure , 1996 .

[16]  P. Nithiarasu,et al.  A novel single domain approach for numerical modelling solid oxide fuel cells , 2010 .

[17]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[18]  A. R. Balakrishnan,et al.  Effects of thermal boundary conditions on natural convection flows within a square cavity , 2006 .

[19]  Fausto Arpino,et al.  Artificial Compressibility-Based CBS Scheme for the Solution of the Generalized Porous Medium Model , 2009 .

[20]  K. N. Seetharamu,et al.  The Finite Element Method , 2005 .

[21]  A. Mohamad,et al.  Three-dimensional double-diffusive convection in a porous cubic enclosure due to opposing gradients of temperature and concentration , 1999, Journal of Fluid Mechanics.

[22]  A. Mauro,et al.  Experimental and Numerical Analysis of Thermal and Hygrometric Characteristics of Building Structures Employing Recycled Plastic Aggregates and Geopolymer Concrete , 2013 .

[23]  Pradip Dutta,et al.  Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures , 2003 .

[24]  A. Sarkar,et al.  FINITE ELEMENT ANALYSIS OF A PARTITIONED CAVITY UNDER MIXED THERMAL CONDITIONS , 1992 .

[25]  Fausto Arpino,et al.  Efficient three-dimensional FEM based algorithm for the solution of convection in partly porous domains , 2011 .

[26]  Ali J. Chamkha,et al.  Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat and mass fluxes and opposing temperature and concentration gradients , 2002 .

[27]  K. N. Seetharamu,et al.  Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall , 1997 .

[28]  Manfred Krafczyk,et al.  Numerical investigation of double-diffusive (natural) convection in vertical annuluses with opposing temperature and concentration gradients , 2010 .

[29]  B. V. Hof,et al.  Asymptotic solution of natural convection problem in a square cavity heated from below , 1996 .

[30]  Ali J. Chamkha,et al.  Natural convection flow under magnetic field in a square cavity for uniformly (or) linearly heated adjacent walls , 2012 .

[31]  Khalil Khanafer,et al.  Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field , 1998 .

[32]  Ching-Jenq Ho,et al.  Numerical study on oscillatory convection of cold water in a tall vertical enclosure , 1999 .

[33]  H. Benmoussa,et al.  Soret and thermosolutal effects on natural convection in a shallow cavity filled with a binary mixture , 2010 .

[34]  Numerical natural convection in a sector‐shaped enclosure , 2001 .

[35]  M. Sheremet,et al.  A numerical simulation of double-diffusive conjugate natural convection in an enclosure , 2011 .

[36]  S. Ostrach,et al.  Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients , 1985 .

[37]  Rui Du,et al.  Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity , 2011 .

[38]  Chi Mei,et al.  Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure , 2004 .

[39]  Hwataik Han,et al.  Double diffusive natural convection in a vertical rectangular enclosure-!. Experimental study , 1991 .

[40]  Fausto Arpino,et al.  A stable explicit fractional step procedure for the solution of heat and fluid flow through interfaces between saturated porous media and free fluids in presence of high source terms , 2010 .

[41]  N. Massarotti,et al.  High Order Explicit Solutions for the Transient Natural Convection of Incompressible Fluids in Tall Cavities , 2014 .

[42]  P. Vasseur,et al.  Multiple steady states in a porous enclosure partially heated and fully salted from below , 2009 .

[43]  Wei-Mon Yan,et al.  MIXED CONVECTION HEAT AND MASS TRANSFER ALONG A VERTICAL WAVY SURFACE , 2003 .

[44]  Fausto Arpino,et al.  High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions , 2010 .